where \(\tau _k(A, \tilde{w})\)  is the necessary algebraic order conditions for the embedded method of order \(\tilde{p}\)  (REF ). Here, we have used \(\tilde{w}\)  to represent the embedded weight obtained numerically. Using MATLAB's fmincon built-in function, we search for \(\tilde{w}\)  that minimizes the cost function best with respect to stability. The positivity constraint on the embedded weights, \(0\le \tilde{w}\le \mathbf {e}\) , is due to Theorem REF  and (REF ). Moreover, we find the above constraints always enforce \(\Vert  D \Vert  \le 1\)  .
For the optimization problem, we do not impose the method to have rational coefficients since many of the optimal SSP methods do not satisfy this restriction - a requirement not enforced by Carpenter, Kennedy, Lewis in [1]}.
